| Abstract
| - Interstellar dust affects many astronomical observations through absorption and reddening, yet this extinction is also a powerful tool for studying interstellar matter in galaxies. Three-dimensional (3D) reconstructions of dust extinction and density in the Milky Way have suffered from artefacts such as the fingers-of-god effect and negative densities, and have been limited by large computational costs. Here, we aim to overcome these issues with a novel algorithm that derives the 3D extinction density of dust in the Milky Way using a latent variable Gaussian process in combination with variational inference. Our model maintains non-negative density and hence monotonically non-decreasing extinction along all lines-of-sight, while performing the inference within a reasonable computational time. Using extinctions for hundreds of thousands of stars computed from optical and near-infrared photometry, together with distances based on Gaia parallaxes, we employ our algorithm to infer the structure of the Orion, Taurus, Perseus, and Cygnus X star-forming regions. A number of features that are superimposed in 2D extinction maps are clearly deblended in 3D dust extinction density maps. For example, we find a large filament on the edge of Orion that may host a number of star clusters. We also identify a coherent structure that may link the Taurus and Perseus regions, and we show that Cygnus X is located at 1300-1500 pc, in line with very-long-baseline interferometry measurements. We compute dust masses of the regions and find these to be slightly higher than previous estimates, likely a consequence of our input data recovering the highest column densities more effectively. By comparing our predicted extinctions to Planck data, we find that known relationships between density and dust processing, where high-extinction lines-of-sight have the most processed grains, hold up in resolved observations when density is included, and that they exist at smaller scales than previously suggested. This can be used to study the changes in size or composition of dust as they are processed in molecular clouds.
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